{"paper":{"title":"A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrea E. F. Clementi, Emanuele Natale, Francesco Pasquale, Giacomo Scornavacca, Luciano Gual\\`a, Mohsen Ghaffari","submitted_at":"2017-07-17T13:10:52Z","abstract_excerpt":"The \\emph{Undecided-State Dynamics} is a well-known protocol for distributed consensus. We analyze it in the parallel \\pull\\ communication model on the complete graph for the \\emph{binary} case (every node can either support one of \\emph{two} possible colors, or be in the undecided state).\n  An interesting open question is whether this dynamics \\emph{always} (i.e., starting from an arbitrary initial configuration) reaches consensus \\emph{quickly} (i.e., within a polylogarithmic number of rounds) in a complete graph with $n$ nodes. Previous work in this setting only considers initial color conf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05135","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}